New Spectral Solutions for High Odd-Order Boundary Value Problems via Generalized Jacobi Polynomials
Sign Up to like & getrecommendations! Published in 2017 at "Bulletin of the Malaysian Mathematical Sciences Society"
DOI: 10.1007/s40840-017-0491-y
Abstract: In this article, some new efficient and accurate algorithms are developed for solving linear and nonlinear odd-order two-point boundary value problems. The algorithm in linear case is based on the application of Petrov–Galerkin method. For… read more here.
Keywords: generalized jacobi; boundary value; odd order; value problems ... See more keywords
A Computational Method Based on Shifted Jacobi Polynomials for the Fractional Differential Equations
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DOI: 10.1007/s44198-025-00273-w
Abstract: In this paper, we present a co-local method based on shifted Jacobi polynomials to obtain approximate solutions to higher-order differential equations. To develop the desired approach by considering the expansion of the fractional problem solution… read more here.
Keywords: differential equations; method; jacobi polynomials; method based ... See more keywords
Lowpass filters approximation based on modified Jacobi polynomials
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DOI: 10.1049/el.2016.3036
Abstract: The orthogonal Jacobi polynomials are not suitable for the characteristic function in the continuous- and discrete-time filter designs because they are not fulfilling the basic conditions: to be pure odd or to be pure even.… read more here.
Keywords: modified jacobi; approximation based; filters approximation; jacobi ... See more keywords
Quadrature Methods for Singular Integral Equations of Mellin Type Based on the Zeros of Classical Jacobi Polynomials
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DOI: 10.3390/axioms12010055
Abstract: In this paper we formulate necessary conditions for the stability of certain quadrature methods for Mellin type singular integral equations on an interval. These methods are based on the zeros of classical Jacobi polynomials, not… read more here.
Keywords: jacobi polynomials; jacobi; quadrature methods; singular integral ... See more keywords
On Polar Jacobi Polynomials
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DOI: 10.3390/math12172767
Abstract: In the present work, we investigate certain algebraic and differential properties of the orthogonal polynomials with respect to a discrete–continuous Sobolev-type inner product defined in terms of the Jacobi measure. read more here.
Keywords: jacobi polynomials; polar jacobi;
Spectral Solutions of Even-Order BVPs Based on New Operational Matrix of Derivatives of Generalized Jacobi Polynomials
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DOI: 10.3390/sym15020345
Abstract: The primary focus of this article is on applying specific generalized Jacobi polynomials (GJPs) as basis functions to obtain the solution of linear and non-linear even-order two-point BVPs. These GJPs are orthogonal polynomials that are… read more here.
Keywords: generalized jacobi; jacobi polynomials; even order; operational matrix ... See more keywords